IV.3

Circular Arc Subdivision

Turkowski Ken,     Apple Computer, Inc. Cupertino, California. E-mail address: turk@apple.com

Introduction

This gem presents an algebraic solution to the rendering problem of circular arcs. These forms commonly arise in graphic design. For instance, well-designed typefaces may apply a very slight curvature on a portion of a letterform to produce a profound aesthetic effect. 1

A circular arc may be represented in terms of the center and radius of its parent circle, plus the starting and ending angles θst and θend. This suggests a first-principles solution that generates successive points on the arc by evaluating the sine and cosine of a series of intermediate angles:

Clearly, this approach is computationally ...

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